Analytic Geometry
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Transcript of Analytic Geometry
What is a function?
It is a relation between a set of inputs and a set of
permissible outputs with the property that each
input is related to exactly one output.
With the function notation y = f(x), each x value
has only one corresponding y value.
The x-values are the inputs, and the y-values
are the outputs.
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Sum of f and g: (f + g)(x) = f(x) + g(x)
Difference of f and g: (f - g)(x) = f(x) - g(x)
Product of f and g: (f . g)(x) = f(x) . g(x)
Quotient of f and g: (f/g)(x) = f(x)/g(x), g(x) not equal to 0
These functions are the ratio of two polynomials. One field of study where they are important is in stability analysis of mechanical and electrical systems (which uses Laplace transforms).
A rational function is a fraction of polynomials. That is,
if p(x) and q(x) are polynomials, thenp(x)
q(x)
A function of the form f(x) = abx
where a = 0 and b>0 ; b = 1 are
real numbers.
Exponential functions are
functions where the variable is
in the exponent.
bx is the inverse function of logb(x)
There are three basic ways to define the trigonometric
functions. Consider a point (x, y) on the terminal side of an
angle θ in standard position. It lies a distance d away from the
origin.
cosine(θ) = cos(θ) = x
d
tangent(θ) = tan(θ) = y
x
d
ycosecant(θ) = csc(θ) =
x
y
secant(θ) = sec(θ) = d
x
cotangent(θ) = cot(θ) =
sine(θ) = sin(θ) = y
d
The six inverse trigonometric functions are arcsine,
arccosine, arctangent, arccosecant, arcsecant, and
arccotangent.